x^2 + 5x +6/
x^2 - 3x -10
How do I do this? Is it asking me to divide?
The answer choices are as following:
A)x + 3/
x - 5
, x ≠ 5
B)x + 3/
x - 5
, x ≠ -2, 5
C)x2 + 5x + 6/
x - 5
, x ≠ 5
D)x2 + 5x + 6/
x - 5
, x ≠ -2, 5
factor it
( x^2 + 5x +6)/( x^2 - 3x -10)
= (x+2)(x+3)/[(x-5)(x+2)]
= (x+3)/(x-5) , x ≠ -2,5
suppose you had (2)(3)/[(3)(7)]
could you not cancel the equal factors to get 2/7
the above question follows the same concept, I canceled the factors (x+2).
x^2 + 5x +6/
x^2 - 3x -10
factor top and bottom
(x+2)(x+3) / [(x-5)(x+2]
= (x+3) / (x-5)
if x = 5 denominator is zero so exclude that point from the domain of x so I say A
Yes, the problem is asking you to divide the first expression (x^2 + 5x + 6) by the second expression (x^2 - 3x - 10). To solve this, you can use long division or synthetic division.
Here's how to do long division:
Step 1: Write the two expressions with a division sign between them.
(x^2 + 5x + 6) / (x^2 - 3x - 10)
Step 2: Divide the first term of the numerator (x^2) by the first term of the denominator (x^2). Write the result above the division line as the first term of the quotient.
x
Step 3: Multiply the entire denominator (x^2 - 3x - 10) by the first term of the quotient (x), and write the result below the numerator.
x(x^2 - 3x - 10) = x^3 - 3x^2 - 10x
Step 4: Subtract the result from the numerator.
(x^2 + 5x + 6) - (x^3 - 3x^2 - 10x) = -4x^2 + 15x + 6
Step 5: Bring down the next term from the numerator (-4x^2) and repeat the process.
(-4x^2 + 15x + 6) / (x^2 - 3x - 10)
Step 6: Divide the first term of the new numerator (-4x^2) by the first term of the denominator (x^2). Write the result above the division line.
-4x
Step 7: Multiply the entire denominator (x^2 - 3x - 10) by the new term (-4x), and write the result below the previous remainder.
-4x(x^2 - 3x - 10) = -4x^3 + 12x^2 + 40x
Step 8: Subtract the result from the new numerator.
(-4x^2 + 15x + 6) - (-4x^3 + 12x^2 + 40x) = -16x^2 - 25x + 6
Step 9: If possible, bring down the next term from the numerator (-16x^2) and repeat the process. In this case, there are no more terms to bring down.
The resulting expression is -16x^2 - 25x + 6. Therefore, the correct answer is:
D) x^2 + 5x + 6 / x - 5, x ≠ -2, 5